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Efficiency is a key issue in any real implementation of a cryptographicprotocol since the physical resources are not unlimited. We will first showthat Quantum Key Distribution is possible with an "Entanglement based" schemewith NPPT symmetric Gaussian states in spite of the fact that these systemscannot be distilled with Gaussian operations (they are all bound entangled). Inthis work we analyze the secrecy properties of Gaussian states under Gaussianoperations. Although such operations are useless for quantum distillation, weprove that it is possible to distill efficiently a secret key secure againstfinite coherent attacks from sufficiently entangled Gaussian states withnon-positive partial transposition. Moreover, all such states allow forefficient key distillation, when the eavesdropper is assumed to performindividual attacks before in an efficient way.

Efficiency in Quantum Key Distribution Protocols using entangled Gaussian states